Download Week 7 - Feb 24

1
Scheduling: CrossChek Golf Club
Manufacturing
• CrossChek sporting goods is considering a process for
development of a new golf club
• Processing times, as well as constraints over when each
step in the process can start are given in the next slide
• CrossChek would like to have a few questions about the
process answered:
• How long does the process take (i.e. the least amount of time)?
• What are the scheduled start and end times for each activity?
• Which activities are critical? That is, which activities must be
completed on time to keep the project on schedule?
• For how long can non-critical activities be delayed?
2
Scheduling Golf Club Production
Activity
Description
Predecessors
Time (days)
A
Planning
--
10
B
Club face forging
A
8
C
Shaft construction
A
14
D
Club head manufacturing
B, C
8
E
Gripping
C
7
F
Assembly
D, E
12
G
Balancing
F
10
3
The Critical Path Method (CPM)
• How can we answer these questions:
• How long does the process take (i.e. the least amount of time)?
• What are the scheduled start and end times for each activity?
• Which activities are critical? That is, which activities must be
completed on time to keep the project on schedule?
• For how long can non-critical activities be delayed?
4
The Critical Path Method (CPM)
• For each activity, let:
• t: the time it takes to complete
• ES: the earliest start time
• EF: the earliest finish time
• LS: the latest start time
• LF: the latest finish time
• Create a predecessor graph, called a project graph
• One node for each activity:
Activity
ES
EF
t
LS
LF
5
The Critical Path Method (CPM)
• “Slack” or “Float”
• The amount of time an activity can be delayed without affecting the
overall project completion time
• Computed by LS – ES or LF – EF
• There will always be a path of activities with no float
• This path is known as the critical path
6
The Critical Path Method (CPM)
• We can now answer these questions:
• How long does the process take (i.e. the least amount of time)?
• 54 days
• What are the scheduled start and end times for each activity?
• See ES, EF for each activity
• Which activities are critical? That is, which activities must be
completed on time to keep the project on schedule?
• Planning-Shaft construction-Club head manufacturing-Assembly-
Balancing
• For how long can non-critical activities be delayed?
• Club face forging: 6 days; Gripping: 1 day
7
Project Acceleration
• CrossChek management finds that the results of the
scheduling analysis are unacceptable, and that the project
must be completed within 50 days. Management
appreciates that project activity times can only be reduced
so much, and that there will be costs associated with
these reductions
8
Crashing
• Commonly used term for project acceleration
• The minimum amount of time in which an activity can be
completed (i.e. under maximum acceleration) is known as
its crash time
• The per-unit cost of accelerating an activity is known as
its crash cost
9
Project Acceleration for CrossChek
Activity
Description
Predecessors
Time
Crash Time
Crash Cost
(1000’s)
A
Planning
--
10
8
400
B
Club face forging
A
8
7
600
C
Shaft construction A
Club head
B, C
manufacturing
14
10
300
8
5
100
D
E
Gripping
C
7
3
200
F
Assembly
D, E
12
9
300
G
Balancing
F
10
8
500
10
LP for CrossChek Crashing Problem
Min 400yA + 600yB + 300yC + 100yD + 200yE + 300yF + 500yG
st
xA + yA > 10
xB + yB - xA > 8
xC + yC - xA > 14
xD + yD - xB > 8
xD + yD - xC > 8
xE + yE - xC > 7
xF + yF - xD > 12
xF + yF - xE > 12
xG + yG - xF > 10
yA < 2
yB < 1
yC < 4
yD < 3
yE < 4
yF < 3
yG < 2
xG < 50
11
LINDO Solution
VARIABLE
YA
YB
YC
YD
YE
YF
YG
XA
XB
XC
XD
XE
XF
XG
VALUE
0.000000
0.000000
0.000000
3.000000
2.000000
1.000000
0.000000
10.000000
24.000000
24.000000
29.000000
29.000000
40.000000
50.000000
REDUCED COST
100.000000
600.000000
0.000000
0.000000
0.000000
0.000000
200.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000